Cinematographic Recording of a Metastable Floating Island in Two- and Three-Dimensional Crystal Growth

Many chemical reactions go through a cascade of events in which a series of metastable intermediates appear, and crystal nucleation is no exception. Although the consensus on the energetics of nucleation suggests the formation of metastable states preceding the crystal growth, little experimental evidence has been reported for their dynamics at an atomistic level. Operando imaging of two-dimensional nucleation on a defect-free NaCl nanocrystal in carbon nanotubes using a millisecond angstrom-resolution transmission electron microscope revealed the formation of a metastable “floating island” (FI) that migrates thermally on the (100) facet of NaCl as the first intermediate of epitaxy. The speed of the migration at 298 K is estimated to be larger than 0.3 nm ms–1. When a crystal tumbles in a container, a space repeatedly forms between the crystal and the container wall that hosts the FI. Tumbling changes the surface energy repeatedly and promotes the conversion of the FI into a new epitaxial layer. We anticipate that this surface catalysis mechanism found on the nanoscale also operates in bulk heterogeneous nucleation where agitation and attrition accelerate crystallization.


TEM image processing
The images taken in a .dm4 format were transformed into 8-bit or 32-bit .tiff format file by Gatan DigitalMicrograph and Fiji software. 1 The data sets recorded on OneView were aligned to minimize specimen drift and rotation by checking the cross-correlation of each image and filtered by a bandpass filter (filtering structures smaller than 5 pixels and larger than 40 pixels, tolerance of direction: 5%). When the moiré pattern of graphitic lattice interferes the NaCl cluster/crystal images, we remove it with the fast Fourier transform software implemented in Fiji software. 2 We herein define 'Binning = X ´ Y ´ T' as combining a cluster of X ´ Y ´ T (X-axis, Y-axis, and time-direction), and pixel binning (4 ´ 4 ´ S3 2 pixels into 1 pixel, pixel resolution 0.020 nm, frame rate 3.38 ms frame -1 ) and lowpass filter (filtering structures smaller than 3 pixels, tolerance of direction: 5%) were applied to the data sets recorded on K3 for smoothing the images. Optimization of the K3 image processing procedure is shown in Figure S1. Linear adjustment of brightness and contrast was applied as required for analyses. Gaussian filter (σx = σy = 2.5 pixels, σz = 0.7 frame) was also applied on processed images for improving visibility for presentation ( Figure S1).

TEM image simulation
Each experimental TEM image was analyzed through comparison with the simulated images of putative models of NaCl crystals in a CNT (NaCl@CNT) seen from various directions. The image simulation was performed by using a multi-slice procedure implemented in a Bionet elbis software. 3 We used the experimental TEM conditions including total electron dose as the parameters for the simulation. The model of NaCl@CNT for the simulation was generated on a MaterialsStudio ® software by fitting a NaCl crystal in a chemical model of CNT whose atomic coordinate was generated to reproduce the outline of the TEM image ( Figure S2). For NaCl we used the effective ionic radii of Na + and Cl -. 4,5

Encapsulation of NaCl in amino-CNT (NaCl@amino-CNT)
Amino-CNT (3.0 mg) 6 was dispersed at 298 K in saturated aqueous NaCl solution (99.5% pure, 1 mL using MilliQ water). After stirring for 24 hours, the reaction mixture was filtered through a PTFE membrane filter (ADVANTEC, pore size: 0.2 μm) and a black filter cake was washed with methanol (1 mL ´ 3). The black powder was placed in vacuo (60 Pa) for 30 minutes to obtain NaCl@amino-CNT (3.1 mg) which was analyzed by single-molecule atomic-resolution time-resolved electron microscopy (SMART-EM).
The black powder of NaCl@amino-CNT forming a large agglomerate was wetted by methanol (2 mL/mg), and gently ground for 3 minutes in an agate mortar so as to break the agglomerate into individual CNT aggregates for TEM analysis. The dispersion was filtered through Kiriyama 5A filter (pore sizes: 7 μm), and the filtrate (10 μL) was drop casted onto a TEM microgrid placed on a paper that absorbed excess methanol. The resulting TEM grid was placed in vacuo (60 Pa) at 298 K for 1 hour.

Measurement of mechanical vibration of CNT
The CNTs underwent stochastic mechanical vibration during TEM observation, for reasons yet to be probed. Mechanical vibration of CNT was evaluated by measuring the position of graphitic wall of CNT (2.0 nm from tip of the CNT) shown in Figure S4. To avoid the influence of Gaussian filtering on the measured values, measurements were conducted on the original images, and the filtered, highly visible images are shown for presentation purposes only (cf., Figure 3a). Due to thermal drift of the specimen from right to left, the displacement gradually decreased.

Correlation between crystal growths and CNT mechanical vibration
In this study, mechanical vibrations with observed displacements larger than 0.1 nm were analyzed. The maximum displacement observed was 0.2 nm, which indicates that two-thirds (i.e., 240°/360°) of the whole vibration was analyzed ( Figure  S5). As shown in Figure 4f, the present analysis shows that 67.6 % of the crystal growths are correlated with the vibration. This result is consistent with the hypothesis that crystal growths are induced by the mechanical vibration of CNT.
TEM images shown in Figure 4 are taken from 8 th event of 9-repetitive crystallization, and not published in our previous report. 7 In the previous paper, we demonstrated the crystallization of 1 st event. Note that manual movement during 3.0-3.3 s in vibrational plot shown in Figure 4c was corrected by subtracting the movement, and the vibrational correlation of E-3 was neglected to avoid any incorrect interpretation.
Computational study on the structure and potential energy for NaCl surface clusters The potential energy difference, ∆U, which was the difference in the potential energy, U, between each r (> 0) and r = 0 (Figure 2g), the distance between the top NaCl layer of the crystal and the cluster in the x direction, d (Figure 2h), and the Na-Cl bond length in the cluster (Figure 2i, j) in the manuscript were obtained with Monte Carlo (MC) simulations in the following way. First, a MC simulation was performed for a system in which a 16-atomic square NaCl cluster was placed at a certain position (r = 0) on one of the two y-z surfaces (x ≥ 0) of the cubic crystal ( Figure 2f). During the MC simulation, the positions of ions in the crystal were fixed at their equilibrium positions at 298 K. The maximum displacement in the trial movement of each ion in the cluster for each of x, y, and z directions was set to 0.01 nm. U, d, and the Na-Cl bond length in the cluster for r = 0 were estimated using 5 × 10 3 configurations, which were obtained at every 4 × 10 2 trial movements of ions after equilibration of 2 × 10 6 trial movements of ions. The final configuration of the cluster in this MC simulation for r = 0 was used as the initial configuration of the cluster in an MC simulation for each r (> 0) along the á100ñ and á110ñ directions.
The MC simulations for r > 0 were also performed using the crystal in which positions of ions was fixed at their equilibrium positions at 298 K. During the MC simulations for r > 0, ions in the cluster were allowed to move only in the x direction with the maximum displacement of 0.03 nm. U, d, and the Na-Cl bond length in the cluster for r > 0 were estimated using 1 × 10 3 configurations, which were obtained at every 1.6 × 10 3 trial movements of ions after equilibration of 4.8 ×10 6 trial movements of ions.
All MC simulations were performed using a standard Metropolis sampling method at a constant temperature of 298 K. The interaction acting on each ion was estimated with a model proposed by Joung and Cheatham. 8 In this model, the interaction between a pair of ions is represented as the Coulomb interaction plus the Lennard-Jones interaction. Calculation of the interaction was performed for all pairs of ions in the system.

Sequential images of NaCl growth taken by K3-IS
Representative 40 frames of lateral growth of NaCl in frame rate of 3.38 ms frame -1 without Gaussian filtering are shown in Figure S3. Sequential 6 frames of migratory epitaxy of NaCl in frame rate of 3.38 ms frame -1 without Gaussian filtering are also shown in Figure S4.     Figure S4. K3-IS images of the NaCl migratory growth in Figure 3. Acceleration voltage 80 kV and EDR of 2.2 ´ 10 6 enm -2 s -1 . Scale bar: 1 nm.

Details in interlayer distance measurements on surface catalyzed epitaxy
Interlayer distances on surface clusters transiently formed in surface-catalyzed epitaxy were statistically analyzed ( Figure S8). The result clearly shows the correlation between d and the mobility of the surface clusters (more mobile cluster exhibits larger d value). 27 individual images are also shown in Figure S9.

Legends for Supplemental Videos
Video S1. Formation of FI and on-site epitaxial growth on a NaCl NC. This is the video of surface migration and subsequent lateral growth of NaCl after processing. The experimental conditions were an acceleration voltage of 80 kV, electron dose rate of 4.6 ´ 10 6 enm -2 s -1 , and exposure time of 3.38 milliseconds for each frame. The playback speed of the video is one-tenth of the original video recording.
Video S2. Millisecond-scale TEM video of the on-site epitaxy without Gaussian filtering. This is the video same with Video S1 before Gaussian filtering. All analyses shown in the main text were conducted on this video. The experimental conditions were an acceleration voltage of 80 kV, electron dose rate of 4.6 ´ 10 6 enm -2 s -1 , and exposure time of 3.38 milliseconds for each frame. The playback speed of the video is one-tenth of the original video recording.
Video S3. Migratory epitaxy of a NaCl NC. This is the video of migratory growth of a NaCl NC after processing. The experimental conditions were an acceleration voltage of 80 kV, electron dose rate of 2.2 ´ 10 6 enm -2 s -1 , and exposure time of 3.38 milliseconds for each frame. The playback speed of the video is one-tenth of the original video recording.